Learning and inverse problems: from theory to solar physics applications

The problem of approximating a function from a set of discrete measurements has been extensively studied since the seventies. Our theoretical analysis proposes a formalization of the function approximation problem which allows dealing with inverse problems and supervised kernel learning as two sides of the same coin. The proposed formalization takes into account arbitrary noisy data (deterministically or statistically defined), arbitrary loss functions (possibly seen as a log-likelihood), handling both direct and indirect measurements. The core idea of this part relies on the analogy between statistical learning and inverse problems. One of the main evidences of the connection occurring across these two areas is that regularization methods, usually developed for ill-posed inverse problems, can be used for solving learning problems. Furthermore, spectral regularization convergence rate analyses provided in these two areas, share the same source conditions but are carried out with either increasing number of samples in learning theory or decreasing noise level in inverse problems. Even more in general, regularization via sparsity-enhancing methods is widely used in both areas and it is possible to apply well-known $ell_1$-penalized methods for solving both learning and inverse problems. In the first part of the Thesis, we analyze such a connection at three levels: (1) at an infinite dimensional level, we define an abstract function approximation problem from which the two problems can be derived; (2) at a discrete level, we provide a unified formulation according to a suitable definition of sampling; and (3) at a convergence rates level, we provide a comparison between convergence rates given in the two areas, by quantifying the relation between the noise level and the number of samples. In the second part of the Thesis, we focus on a specific class of problems where measurements are distributed according to a Poisson law. We provide a data-driven, asymptotically unbiased, and globally quadratic approximation of the Kullback-Leibler divergence and we propose Lasso-type methods for solving sparse Poisson regression problems, named PRiL for Poisson Reweighed Lasso and an adaptive version of this method, named APRiL for Adaptive Poisson Reweighted Lasso, proving consistency properties in estimation and variable selection, respectively. Finally we consider two problems in solar physics: 1) the problem of forecasting solar flares (learning application) and 2) the desaturation problem of solar flare images (inverse problem application). The first application concerns the prediction of solar storms using images of the magnetic field on the sun, in particular physics-based features extracted from active regions from data provided by Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). The second application concerns the reconstruction problem of Extreme Ultra-Violet (EUV) solar flare images recorded by a second instrument on board SDO, the Atmospheric Imaging Assembly (AIA). We propose a novel sparsity-enhancing method SE-DESAT to reconstruct images affected by saturation and diffraction, without using any a priori estimate of the background solar activity

A consistent and numerically efficient variable selection method for sparse Poisson regression with applications to learning and signal recovery

We propose an adaptive 1-penalized estimator in the framework of Generalized Linear Models with identity-link and Poisson data, by taking advantage of a globally quadratic approximation of the Kullback-Leibler divergence. We prove that this approximation is asymptotically unbiased and that the proposed estimator has the variable selection consistency property in a deterministic matrix design framework. Moreover, we present a numerically efficient strategy for the computation of the proposed estimator, making it suitable for the analysis of massive counts datasets. We show with two numerical experiments that the method can be applied both to statistical learning and signal recovery problems

EigenScape : A Database of Spatial Acoustic Scene Recordings

The classification of acoustic scenes and events is an emerging area of research in the field of machine listening. Most of the research conducted so far uses spectral features extracted from monaural or stereophonic audio rather than spatial features extracted from multichannel recordings. This is partly due to the lack thus far of a substantial body of spatial recordings of acoustic scenes. This paper formally introduces EigenScape, a new database of fourth-order Ambisonic recordings of eight different acoustic scene classes. The potential applications of a spatial machine listening system are discussed before detailed information on the recording process and dataset are provided. A baseline spatial classification system using directional audio coding (DirAC) techniques is detailed and results from this classifier are presented. The classifier is shown to give good overall scene classification accuracy across the dataset, with 7 of 8 scenes being classified with an accuracy of greater than 60% with an 11% improvement in overall accuracy compared to use of Mel-frequency cepstral coefficient (MFCC) features. Further analysis of the results shows potential improvements to the classifier. It is concluded that the results validate the new database and show that spatial features can characterise acoustic scenes and as such are worthy of further investigatio

Bad and good errors: value-weighted skill scores in deep ensemble learning

In this paper we propose a novel approach to realize forecast verification. Specifically, we introduce a strategy for assessing the severity of forecast errors based on the evidence that, on the one hand, a false alarm just anticipating an occurring event is better than one in the middle of consecutive non-occurring events, and that, on the other hand, a miss of an isolated event has a worse impact than a miss of a single event, which is part of several consecutive occurrences. Relying on this idea, we introduce a novel definition of confusion matrix and skill scores giving greater importance to the value of the prediction rather than to its quality. Then, we introduce a deep ensemble learning procedure for binary classification, in which the probabilistic outcomes of a neural network are clustered via optimization of these value-weighted skill scores. We finally show the performances of this approach in the case of three applications concerned with pollution, space weather and stock prize forecasting

A comprehensive theoretical framework for the optimization of neural networks classification performance with respect to weighted metrics

In many contexts, customized and weighted classification scores are designed in order to evaluate the goodness of the predictions carried out by neural networks. However, there exists a discrepancy between the maximization of such scores and the minimization of the loss function in the training phase. In this paper, we provide a complete theoretical setting that formalizes weighted classification metrics and then allows the construction of losses that drive the model to optimize these metrics of interest. After a detailed theoretical analysis, we show that our framework includes as particular instances well-established approaches such as classical cost-sensitive learning, weighted cross entropy loss functions and value-weighted skill scores

El principio de igualdad y no discriminación en las relaciones laborales: perspectiva constitucional reciente

Artikulu honetan, Auzitegi Konstituzionalak lan-harremanetako berdintasuneko printzipioari eta bereizkeriarik ezaren printzipioari begira zer-nolako doktrina teoriko eta praktikoa darabilen aztertuko dugu, labur-labur eta modu deskriptiboan.Arreta berezia eskainiko diogu Auzitegi horrek zenbait gaietan izandako jarreraren bilakaerari (emakume haurdunen kaleratzea, enpresaburuek haurdun daudela jakin gabe; sexu-jazarpena; ekintza positiboak; familia eta lana bateratzeko eskubideak). Zuzenbide substantiboa aztertzeaz gain, Auzitegi Konstituzionalaren aurrean babes eskeko errekurtsoaren bidez egiten den tutoretza-prozesua landuko dugu.; This paper exams, briefly and descriptive, the Constitutional Court"s doctrine on the principle of equality and nondiscrimination in employment relations. Special attention is paid to the evolution of the position of this Court concerning the dismissal of pregnant women when the employer doesn"t know that fact, sexual harassment, positive actions and family leaves. The paper also studies the writ of amparo, a remedy for the protection of these rights at the Constitutional Court.; En el presente artículo se analiza de modo breve y descriptivo la doctrina teórica y práctica del Tribunal Constitucional en relación con el principio de igualdad y de no discriminación en las relaciones laborales. Con especial atención a la evolución de la posición de este Tribunal en relación con el despido de la mujer embarazada cuando el empresario desconoce dicha circunstancia, con el acoso sexual, con las acciones positivas y los derechos de conciliación. Junto al estudio del derecho sustantivo, se aborda el proceso de tutela ante el Tribunal constitucional mediante el recurso de amparo

Contraterrorismo en el Sahel: Cumplimiento con un régimen internacional en formación

El terrorismo constituye una de las denominadas “nuevas amenazas” que conforman actualmente la agenda de seguridad internacional. Empero, no todos los Estados poseen la misma capacidad para luchar en contra del mismo, y el contraterrorismo se convierte así en un área importante para la cooperación interestatal. Tomando en cuenta la disponibilidad de fondos, la naturaleza del régimen político, la existencia de ataques terroristas en el territorio nacional y las propias capacidades estatales en Burkina Faso, Chad, Mali y Níger en el año 2017, la tesis intenta elucidar qué factores afectan el cumplimiento de dichos países con el régimen internacional contraterrorista emergente